{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/solvability-of-matrix-riccati-inequalities","title":"Solvability of Matrix Riccati Inequalities","arxiv_id":"1505.04861","date":"2015-05-19","proceeding":null,"authors":["Kevin Kissi"],"abstract":"We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati inequalities is a subject of the famous Kalman- Yakubovich lemma. This paper presents necessary and sufficient conditions for solvability of Riccati inequality in the general sign indefinite case. To this end we use special representations of Hamiltonian matrices. The results are illustrated by an example.","url_abs":"http://arxiv.org/abs/1505.04861v1","url_pdf":"http://arxiv.org/pdf/1505.04861v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"solvability-of-matrix-riccati-inequalities","repo_url":"https://github.com/kevinkissi/solvability-of-matrix-riccati-inequality","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}